onegirl

2 years ago

Hmm I think you've done a few of these types of problems.
So I'm just curious, which result makes more sense to you.
Seeing our tangent line in slope-intercept form: \(\large y=mx+b\),
Or in point-slope form: \(\large y-y_o=m(x-x_o)\).

Ok we will have 2 pieces we need to find.
\(\large m\) is the slope of our tangent line.
Take the derivative of your function, and evaluate it at \(\large x=\pi/8\). That will be your \(\large m\) value.

To find it, we'll need to plug in a coordinate pair that falls on the line.
Well, since our line is tangent to the curve at x=pi/8, we can plug x=pi/8 into that function to get a corresponding y value. This will be the coordinate pair we'll plug into our tangent line.